I am curious concerning your data. I trace my lineage through Hermmanius Ache (in recent generations pronounched "ah-key" and often anglicized to "Achey") who arrived in Philadelphia, Pa. in 1752. There is some difficulty in tracing the complete family lineage as there are more people of the Ache in colonial Pennsylvania than can be accomodated by the widely available ships registries (ex. Penn. German Pioneers).
It would seem to me that the surname Ache might well derive from the norse Ake (as in Akerman, which is still common enough in modern Scandinavia) though there are scattered indications of the surname existing in Prussia, Holland and France.
This name as a transliteration of "Egg" opens up a new avenue of thought. Perhaps you can provide some insight?